Tomás Veloz 

Bionote:

Tomas Veloz has a PhD in Interdisciplinary Studies and a Master's degree in Computer Science, with majors in Mathematics and Physics. His research focuses on interdisciplinary mathematical modeling. His main research areas are Chemical Organization theory, where he has proven mathematical results such as the decomposition theorem and the existence of quantum-like organizational structures, and quantum cognition, where he has developed methods to represent collections of concepts in a Hilbert Space, and has shown that various cognitive and language phenomena exhibit quantum structure. Dr. Veloz is the Founder and Director of the Foundation for the Interdisciplinary Development of Science, Technology and Arts (DICTA), Chile, which collaborates with various institutions around the world for the generation and dissemination of integrated knowledge, and the development of projects with social impact. 

Can Ecological Communities be Modeled as Autopoietic Reaction Networks?

Abstract

Understanding how species coexist within ecological communities is a fundamental question in ecology. Traditionally, the focus has been on individuals as the biological units driving interactions within a community. These interactions, in turn, are shaped by the properties of species, creating a dynamic interplay. The abiotic environment also plays a crucial role, acting as a conditioning space that further influences the structuring of the community. While various modeling frameworks have been employed to study ecological communities, none have been able to simultaneously address the challenges of handling large-scale systems, providing detailed interaction mechanisms, and facilitating meaningful model comparisons at the analytical level, i.e. beyond simulation outcomes.

In this talk, we propose a paradigm shift by introducing the language of reaction networks, a concept native to systems biology. Unlike existing frameworks, reaction networks consider both species and abiotic environment as equally important components, with the focus shifting from specific species interactions to more general processes governing the persistence of the entire community. We demonstrate how this novel approach, particularly within the framework of Chemical Organization Theory (COT), offers a powerful analytical toolset to investigate the relationship between ecological system structure and stability. By computationally identifying closed and self-maintaining sub-collections of species, known as organizations, COT unveils groups of species that can coexist over the long-term. The set of organizations encompasses all potential stable regimes in the ecological system dynamics, and can be used to formalize a "multidimensional" view of the concept of resilience in ecology.

Furthermore, we illustrate some other mathematical properties that reveal interesting connections between ecology, logic and computation,  showcasing the potential of COT to introduce innovative mathematical tools for ecological modeling.

Chemical Organization Theory

Abstract

Chemical Organization Theory (COT) is a method to study reaction networks. Its focus is relating structure with dynamical stability in very large systems. The reason is that in those cases the dynamical stability properties cannot be obtained from analytical solutions and simulations are of limited use. 

We will first review the basics of reaction networks and the fundamental properties needed to define organizations, the fundamental object of study of the theory. Namely, we will define connectivity, productive closure and self-maintainance of a reaction network using illustrative examples. Next, we will show a structural result known as the decomposition theorem for organizations, which allows to separate an organization into parts that are weakly overlapped and can be ensured to not alter each other in the face of a structural change. We will introduce a python library to use and explore COT along the tutorial so users can later try their own models.